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    This single-source volume provides authoritative discussions on the classical foundations of, and specialized topics in, field theory - giving a clear and comprehensive overview on current developments in this constantly growing area. Beginning with a thorough summary of field theory that emphasizes refinements and extensions achieved in recent studies, 'Field Theory' describes canonical fundamental units of certain classes of pure cubic fields, proves Kneser's theorem on torsion groups of separable field extensions, establishes a theorem that provides necessary and sufficient conditions for the Galois group of a binomial X[superscript n]-a to be abelian, shows the result of the degrees of sums in a separable field extension, and more. Proceeding to a detailed examination of multiplicative groups of fields, this monograph investigates the isomorphism class of F*, where F is a distinguished field such as local or global , proves Brandis's theorem, which asserts that if F is infinite and E[not equal]F, then E*/F* is not finitely generated, and gives a complete accounting of May's contributions to multiplicative groups of fields. Providing numerous examples to illustrate that the results obtained are the best possible, 'Field Theory' is an important reference for all mathematicians, especially algebraists and number theorists, and text for graduate students in algebra courses.

    Detalhes do Produto

      • Ano de Edição: 1989
      • Ano:  1989
      • País de Produção: United States
      • Código de Barras:  9780824780296
      • ISBN:  0824780299
      • Encadernação:  ENCADERNADO
      • Altura: 26.70 cm
      • Largura: 19.10 cm
      • Nº de Páginas:  568

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